Class: PerfectShape::CubicBezierCurve

Inherits:
Shape
  • Object
show all
Includes:
MultiPoint
Defined in:
lib/perfect_shape/cubic_bezier_curve.rb

Constant Summary collapse

OUTLINE_MINIMUM_DISTANCE_THRESHOLD = 
BigDecimal('0.001')

Instance Attribute Summary

Attributes included from MultiPoint

#points

Class Method Summary collapse

Instance Method Summary collapse

Methods included from MultiPoint

#first_point, #initialize, #max_x, #max_y, #min_x, #min_y, normalize_point_array

Methods inherited from Shape

#==, #bounding_box, #center_point, #center_x, #center_y, #height, #max_x, #max_y, #min_x, #min_y, #width

Class Method Details

.point_crossings(x1, y1, xc1, yc1, xc2, yc2, x2, y2, px, py, level = 0) ⇒ Object

Calculates the number of times the cubic bézier curve from (x1,y1) to (x2,y2) crosses the ray extending to the right from (x,y). If the point lies on a part of the curve, then no crossings are counted for that intersection. the level parameter should be 0 at the top-level call and will count up for each recursion level to prevent infinite recursion +1 is added for each crossing where the Y coordinate is increasing -1 is added for each crossing where the Y coordinate is decreasing



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# File 'lib/perfect_shape/cubic_bezier_curve.rb', line 37

def point_crossings(x1, y1, xc1, yc1, xc2, yc2, x2, y2, px, py, level = 0)
  return 0 if (py <  y1 && py <  yc1 && py <  yc2 && py <  y2)
  return 0 if (py >= y1 && py >= yc1 && py >= yc2 && py >= y2)
  # Note y1 could equal yc1...
  return 0 if (px >= x1 && px >= xc1 && px >= xc2 && px >= x2)
  if (px <  x1 && px <  xc1 && px <  xc2 && px <  x2)
    if (py >= y1)
      return 1 if (py < y2)
    else
      # py < y1
      return -1 if (py >= y2)
    end
    # py outside of y12 range, and/or y1==yc1
    return 0
  end
  # double precision only has 52 bits of mantissa
  return PerfectShape::Line.point_crossings(x1, y1, x2, y2, px, py) if (level > 52)
  xmid = BigDecimal((xc1 + xc2).to_s) / 2
  ymid = BigDecimal((yc1 + yc2).to_s) / 2
  xc1 = BigDecimal((x1 + xc1).to_s) / 2
  yc1 = BigDecimal((y1 + yc1).to_s) / 2
  xc2 = BigDecimal((xc2 + x2).to_s) / 2
  yc2 = BigDecimal((yc2 + y2).to_s) / 2
  xc1m = BigDecimal((xc1 + xmid).to_s) / 2
  yc1m = BigDecimal((yc1 + ymid).to_s) / 2
  xmc1 = BigDecimal((xmid + xc2).to_s) / 2
  ymc1 = BigDecimal((ymid + yc2).to_s) / 2
  xmid = BigDecimal((xc1m + xmc1).to_s) / 2
  ymid = BigDecimal((yc1m + ymc1).to_s) / 2
  # [xy]mid are NaN if any of [xy]c0m or [xy]mc1 are NaN
  # [xy]c0m or [xy]mc1 are NaN if any of [xy][c][01] are NaN
  # These values are also NaN if opposing infinities are added
  return 0 if (xmid.nan? || ymid.nan?)
  point_crossings(x1, y1, xc1, yc1, xc1m, yc1m, xmid, ymid, px, py, level+1) +
    point_crossings(xmid, ymid, xmc1, ymc1, xc2, yc2, x2, y2, px, py, level+1)
end

Instance Method Details

#contain?(x_or_point, y = nil, outline: false, distance_tolerance: 0) ⇒ Boolean

Checks if cubic bézier curve contains point (two-number Array or x, y args)

the cubic bézier curve, false if the point lies outside of the cubic bézier curve’s bounds.

Parameters:

  • x —

    The X coordinate of the point to test.

  • y (defaults to: nil) —

    The Y coordinate of the point to test.

Returns:

  • (Boolean) —

    true if the point lies within the bound of



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# File 'lib/perfect_shape/cubic_bezier_curve.rb', line 88

def contain?(x_or_point, y = nil, outline: false, distance_tolerance: 0)
  x, y = Point.normalize_point(x_or_point, y)
  return unless x && y
  
  if outline
    distance_tolerance = BigDecimal(distance_tolerance.to_s)
    minimum_distance_threshold = OUTLINE_MINIMUM_DISTANCE_THRESHOLD + distance_tolerance
    point_distance(x, y, minimum_distance_threshold: minimum_distance_threshold) < minimum_distance_threshold
  else
    # Either x or y was infinite or NaN.
    # A NaN always produces a negative response to any test
    # and Infinity values cannot be "inside" any path so
    # they should return false as well.
    return false if (!(x * 0.0 + y * 0.0 == 0.0))
    # We count the "Y" crossings to determine if the point is
    # inside the curve bounded by its closing line.
    x1 = points[0][0]
    y1 = points[0][1]
    x2 = points[3][0]
    y2 = points[3][1]
    line = PerfectShape::Line.new(points: [[x1, y1], [x2, y2]])
    crossings = line.point_crossings(x, y) + point_crossings(x, y)
    (crossings & 1) == 1
  end
end

#curve_center_point ⇒ Object

The center point on the outline of the curve



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# File 'lib/perfect_shape/cubic_bezier_curve.rb', line 129

def curve_center_point
  subdivisions.last.points[0]
end

#curve_center_x ⇒ Object

The center point x on the outline of the curve



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# File 'lib/perfect_shape/cubic_bezier_curve.rb', line 134

def curve_center_x
  subdivisions.last.points[0][0]
end

#curve_center_y ⇒ Object

The center point y on the outline of the curve



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# File 'lib/perfect_shape/cubic_bezier_curve.rb', line 139

def curve_center_y
  subdivisions.last.points[0][1]
end

#intersect?(rectangle) ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/perfect_shape/cubic_bezier_curve.rb', line 215

def intersect?(rectangle)
  w = rectangle.width
  h = rectangle.height
  
  # Trivially reject non-existant rectangles
  return false if w <= 0 || h <= 0

  num_crossings = rectangle_crossings(rectangle)
  # the intended return value is
  # num_crossings != 0 || num_crossings == PerfectShape::Rectangle::RECT_INTERSECTS
  # but if (num_crossings != 0) num_crossings == INTERSECTS won't matter
  # and if !(num_crossings != 0) then num_crossings == 0, so
  # num_crossings != RECT_INTERSECT
  num_crossings != 0
end

#point_crossings(x_or_point, y = nil, level = 0) ⇒ Object

Calculates the number of times the cubic bézier curve crosses the ray extending to the right from (x,y). If the point lies on a part of the curve, then no crossings are counted for that intersection. the level parameter should be 0 at the top-level call and will count up for each recursion level to prevent infinite recursion +1 is added for each crossing where the Y coordinate is increasing -1 is added for each crossing where the Y coordinate is decreasing



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# File 'lib/perfect_shape/cubic_bezier_curve.rb', line 122

def point_crossings(x_or_point, y = nil, level = 0)
  x, y = Point.normalize_point(x_or_point, y)
  return unless x && y
  CubicBezierCurve.point_crossings(points[0][0], points[0][1], points[1][0], points[1][1], points[2][0], points[2][1], points[3][0], points[3][1], x, y, level)
end

#point_distance(x_or_point, y = nil, minimum_distance_threshold: OUTLINE_MINIMUM_DISTANCE_THRESHOLD) ⇒ Object 



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# File 'lib/perfect_shape/cubic_bezier_curve.rb', line 185

def point_distance(x_or_point, y = nil, minimum_distance_threshold: OUTLINE_MINIMUM_DISTANCE_THRESHOLD)
  x, y = Point.normalize_point(x_or_point, y)
  return unless x && y
  
  point = Point.new(x, y)
  current_curve = self
  minimum_distance = point.point_distance(curve_center_point)
  last_minimum_distance = minimum_distance + 1 # start bigger to ensure going through loop once at least
  while minimum_distance >= minimum_distance_threshold && minimum_distance < last_minimum_distance
    curve1, curve2 = current_curve.subdivisions
    curve1_center_point = curve1.curve_center_point
    distance1 = point.point_distance(curve1_center_point)
    curve2_center_point = curve2.curve_center_point
    distance2 = point.point_distance(curve2_center_point)
    last_minimum_distance = minimum_distance
    if distance1 < distance2
      minimum_distance = distance1
      current_curve = curve1
    else
      minimum_distance = distance2
      current_curve = curve2
    end
  end
  if minimum_distance < minimum_distance_threshold
    minimum_distance
  else
    last_minimum_distance
  end
end

#rect_crossings(rxmin, rymin, rxmax, rymax, level, crossings = 0) ⇒ Object

Accumulate the number of times the cubic crosses the shadow extending to the right of the rectangle. See the comment for the RECT_INTERSECTS constant for more complete details.

crossings arg is the initial crossings value to add to (useful in cases where you want to accumulate crossings from multiple shapes)



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# File 'lib/perfect_shape/cubic_bezier_curve.rb', line 259

def rect_crossings(rxmin, rymin, rxmax, rymax, level, crossings = 0)
  x0 = points[0][0]
  y0 = points[0][1]
  xc0 = points[1][0]
  yc0 = points[1][1]
  xc1 = points[2][0]
  yc1 = points[2][1]
  x1 = points[3][0]
  y1 = points[3][1]
  
  return crossings if y0 >= rymax && yc0 >= rymax && yc1 >= rymax && y1 >= rymax
  return crossings if y0 <= rymin && yc0 <= rymin && yc1 <= rymin && y1 <= rymin
  return crossings if x0 <= rxmin && xc0 <= rxmin && xc1 <= rxmin && x1 <= rxmin
  if x0 >= rxmax && xc0 >= rxmax && xc1 >= rxmax && x1 >= rxmax
    # Cubic is entirely to the right of the rect
    # and the vertical range of the 4 Y coordinates of the cubic
    # overlaps the vertical range of the rect by a non-empty amount
    # We now judge the crossings solely based on the line segment
    # connecting the endpoints of the cubic.
    # Note that we may have 0, 1, or 2 crossings as the control
    # points may be causing the Y range intersection while the
    # two endpoints are entirely above or below.
    if y0 < y1
      # y-increasing line segment...
      crossings += 1 if (y0 <= rymin && y1 >  rymin)
      crossings += 1 if (y0 <  rymax && y1 >= rymax)
    elsif y1 < y0
      # y-decreasing line segment...
      crossings -= 1 if (y1 <= rymin && y0 >  rymin)
      crossings -= 1 if (y1 <  rymax && y0 >= rymax)
    end
    return crossings
  end
  # The intersection of ranges is more complicated
  # First do trivial INTERSECTS rejection of the cases
  # where one of the endpoints is inside the rectangle.
  return PerfectShape::Rectangle::RECT_INTERSECTS if ((x0 > rxmin && x0 < rxmax && y0 > rymin && y0 < rymax) ||
    (x1 > rxmin && x1 < rxmax && y1 > rymin && y1 < rymax))
      
  # Otherwise, subdivide and look for one of the cases above.
  # double precision only has 52 bits of mantissa
  return PerfectShape::Line.new(points: [[x0, y0], [x1, y1]]).rect_crossings(rxmin, rymin, rxmax, rymax, crossings) if (level > 52)
  xmid = BigDecimal((xc0 + xc1).to_s) / 2
  ymid = BigDecimal((yc0 + yc1).to_s) / 2
  xc0 = BigDecimal((x0 + xc0).to_s) / 2
  yc0 = BigDecimal((y0 + yc0).to_s) / 2
  xc1 = BigDecimal((xc1 + x1).to_s) / 2
  yc1 = BigDecimal((yc1 + y1).to_s) / 2
  xc0m = BigDecimal((xc0 + xmid).to_s) / 2
  yc0m = BigDecimal((yc0 + ymid).to_s) / 2
  xmc1 = BigDecimal((xmid + xc1).to_s) / 2
  ymc1 = BigDecimal((ymid + yc1).to_s) / 2
  xmid = BigDecimal((xc0m + xmc1).to_s) / 2
  ymid = BigDecimal((yc0m + ymc1).to_s) / 2
  # [xy]mid are NaN if any of [xy]c0m or [xy]mc1 are NaN
  # [xy]c0m or [xy]mc1 are NaN if any of [xy][c][01] are NaN
  # These values are also NaN if opposing infinities are added
  return 0 if xmid.nan? || ymid.nan?
  cubic1 = CubicBezierCurve.new(points: [[x0, y0], [xc0, yc0], [xc0m, yc0m], [xmid, ymid]])
  crossings = cubic1.rect_crossings(rxmin, rymin, rxmax, rymax, level + 1, crossings)
  if crossings != PerfectShape::Rectangle::RECT_INTERSECTS
    cubic2 = CubicBezierCurve.new(points: [[xmid, ymid], [xmc1, ymc1], [xc1, yc1], [x1, y1]])
    crossings = cubic2.rect_crossings(rxmin, rymin, rxmax, rymax, level + 1, crossings)
  end
  crossings
end

#rectangle_crossings(rectangle) ⇒ Object 



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# File 'lib/perfect_shape/cubic_bezier_curve.rb', line 231

def rectangle_crossings(rectangle)
  x = rectangle.x
  y = rectangle.y
  w = rectangle.width
  h = rectangle.height
  x1 = points[0][0]
  y1 = points[0][1]
  x2 = points[3][0]
  y2 = points[3][1]

  crossings = 0
  if !(x1 == x2 && y1 == y2)
    line = PerfectShape::Line.new(points: [[x1, y1], [x2, y2]])
    crossings = line.rect_crossings(x, y, x+w, y+h, crossings)
    return crossings if crossings == PerfectShape::Rectangle::RECT_INTERSECTS
  end
  # we call this with the curve's direction reversed, because we wanted
  # to call rectCrossingsForLine first, because it's cheaper.
  rect_crossings(x, y, x+w, y+h, 0, crossings)
end

#subdivisions(level = 1) ⇒ Object

Subdivides CubicBezierCurve exactly at its curve center returning 2 CubicBezierCurve’s as a two-element Array by default

Optional ‘level` parameter specifies the level of recursions to perform to get more subdivisions. The number of resulting subdivisions is 2 to the power of `level` (e.g. 2 subdivisions for level=1, 4 subdivisions for level=2, and 8 subdivisions for level=3)



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# File 'lib/perfect_shape/cubic_bezier_curve.rb', line 150

def subdivisions(level = 1)
  level -= 1 # consume 1 level
  
  x1 = points[0][0]
  y1 = points[0][1]
  ctrlx1 = points[1][0]
  ctrly1 = points[1][1]
  ctrlx2 = points[2][0]
  ctrly2 = points[2][1]
  x2 = points[3][0]
  y2 = points[3][1]
  centerx = BigDecimal((ctrlx1 + ctrlx2).to_s) / 2
  centery = BigDecimal((ctrly1 + ctrly2).to_s) / 2
  ctrlx1 = BigDecimal((x1 + ctrlx1).to_s) / 2
  ctrly1 = BigDecimal((y1 + ctrly1).to_s) / 2
  ctrlx2 = BigDecimal((x2 + ctrlx2).to_s) / 2
  ctrly2 = BigDecimal((y2 + ctrly2).to_s) / 2
  ctrlx12 = BigDecimal((ctrlx1 + centerx).to_s) / 2
  ctrly12 = BigDecimal((ctrly1 + centery).to_s) / 2
  ctrlx21 = BigDecimal((ctrlx2 + centerx).to_s) / 2
  ctrly21 = BigDecimal((ctrly2 + centery).to_s) / 2
  centerx = BigDecimal((ctrlx12 + ctrlx21).to_s) / 2
  centery = BigDecimal((ctrly12 + ctrly21).to_s) / 2
  
  first_curve = CubicBezierCurve.new(points: [x1, y1, ctrlx1, ctrly1, ctrlx12, ctrly12, centerx, centery])
  second_curve = CubicBezierCurve.new(points: [centerx, centery, ctrlx21, ctrly21, ctrlx2, ctrly2, x2, y2])
  default_subdivisions = [first_curve, second_curve]
  
  if level == 0
    default_subdivisions
  else
    default_subdivisions.map { |curve| curve.subdivisions(level) }.flatten
  end
end